Question

what is the direction of the force acting on a negatively charged particle moving from east to west in a magnetic field directed towards ​

Answer 1

To find:

Direction of the force acting on a negatively charged particle moving from east to west in a magnetic field directed towards north.

Calculation:

Let's consider charge -q is travelling towards west.

So, its Velocity vector will be $\vec{v}=v(-\hat{i})$

Again, the magnetic field is directed towards north, hence the magnetic field vector will be $\vec{B} = B \hat{j}$

So, net force vector:

$\therefore \: \rm{ \vec{F} = ( - q) \bigg \{ \vec{v} \times \vec{B} \bigg \}}$

$= > \: \rm{ \vec{F} = ( - q) \bigg \{ v ( - \hat{i}) \times B( \hat{j}) \bigg \}}$

$= > \: \rm{ \vec{F} = ( - q) \bigg \{ v B( - \hat{k}) \bigg \}}$

$= > \: \rm{ \vec{F} = q \bigg \{ v B( \hat{k}) \bigg \}}$

$= > \: \rm{ \vec{F} = q v B \: ( \hat{k}) }$

So, the force vector will be directed upwards.

• This question can also be solved using Fleming's left hand rule.

• The index finger will denote the magnetic field, the middle finger will denote the direction of current (opposite to direction of movement of electron) and the thumb will direct the force.

Hope It Helps.

Answer 2

Direction of negatively charged particles =Towards West

$\sf \red{Direction~ of~ current~ is~always~ opposite~ to}$

$\sf \red{direction ~of ~negatively~charged~ particles.}$

⋆ Direction of current = Towards east

⋆ Direction of magnetic field =Towards North

$\boxed{\rm{\purple{Fleming's~ Left~ Hand~ Rule}}}$

⋆ Direction of force = $\rm {\underline{\green {Upwards}}}.$